Abstract A08: Histologic evidence for a bio-mathematical model of glioblastoma invasion

Purpose: Investigate the utility of patient-specific spatial predictions of tumor cell density from a bio-mathematical model. Introduction: Glioblastomas (GBMs) are the most malignant of all primary brain tumors. While it is known there is always a non-detectable portion of the tumor, current techniques of monitoring GBM progression, imaging and initial histological assessment, are not able to reliably estimate the tumor invasion past the enhancing region on T2-Weighted (T2W) imaging. Over the last two decades, a large effort has been made to create a simple patient-specific mathematical model of gliomas. The resulting model, referred to as the Proliferation-Invasion (PI) model, is based on two key parameters, the net growth rate, ρ, and the dispersal coefficient, D. In this model, the ratio of D/ρ is related to degree of invasion and the product D*ρ, is related to the speed of growth. The intuitive understanding provided by this model has been able to provide patient-specific understanding of disease kinetics enabling prediction of outcomes following surgical resection, radiation and the development of a prognostic response metric. Previous literature utilizing this model has been based on the assumption that what is seen on the pretreatment T1-Weighted contrast-enhanced (T1Gd) and T2W, images correspond to an 80% and 16% tumor cell density threshold respectively. This assumption allows for an estimate of D/ρ from a single time point of imaging. While these values were based on extensive experience, for ethical and technical reasons, they have never been rigorously investigated histologically. Recent technological advances have made it possible for surgeons to use an MRI to guide the acquisition of tissue making it possible to know with a good degree of accuracy where on the MR image the histological specimen comes from. Methods: Model Calibration : To estimate D/ρ for each patient, we assume abnormalities on the T1Gd and T2W images correspond to an 80% and 16% tumor cell density threshold respectively. We then utilize a Bayesian calibration approach based on adaptive grid refinement while holding the velocity constant to find the most likely value of D/ρ to match the observed radial measurements. Three-Dimensional Density Maps : Given a gray/white segmentation and an estimate for D/ρ, we can build a tumor cell density prediction in the patient's anatomy using the Eikonal equations and the modified Fast Marching Method (FMM) algorithm presented by Konukog